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Greenwood statistic ：ウィキペディア英語版

Greenwood statistic
The Greenwood statistic is a spacing statistic and can be used to evaluate clustering of events in time or locations in space.〔Greenwood, Major (1946) The Statistical Study of Infectious Diseases. ''Journal of the Royal Statistical Society'', 109(2): 85–110. 〕
==Definition==
In general, for a given sequence of events in time or space the statistic is given by:.〔
:

G(n)=\sum^_D^2_i ,

where

D_i

represents the interval between events or points in space and is a number between 0 and 1 such that the sum of all

D_i = 1

.
Where intervals are given by numbers that do not represent a fraction of the time period or distance, the Greenwood statistic is modified 〔D'Agostino, Ralph B. and Stephens, Michael A. (1986) ''Goodness-of-fit techniques'', Marcel Dekker, Inc., New York 〕 and is given by:
:

G(n)=\fracX^2_i} ,

where:
:

T_n=\sum^_X_i,

and

X_i

represents the length of the i''th interval, which is either the time between events or the distances between points in space.
A reformulation of the statistic yields
:

G(n)=\tfrac (\tfracC_v^2+1) ,

where

C_v

is the sample coefficient of variation of the ''n'' + 1 interval lengths.

抄文引用元・出典: フリー百科事典『ウィキペディア（Wikipedia）』
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